Questions tagged [svd]

Singular Value Decomposition (SVD) is a decomposition (factorization) of rectangular real or complex matrix into the product of a unitary rotation matrix, a diagonal scaling matrix, and a second unitary rotation matrix.

84 questions
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What is the fastest way to compute the sum of the singular values of a matrix?

Is there a faster way to compute the nuclear norm (trace norm, sum of singular values) of a matrix A than computing SVD(A) directly (or diagonalizing A^*A)? I am particularly interested in the case where A is square. Assuming that A is real would…
Brent
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Singular vectors of s1 for tiny dense matrices

I have a function whose main bottleneck is finding a(ny) singular vector pair in the space of the largest singular value, along with the singular value itself. This is done a huge number of times. This is the structure I know about: Tiny. 4x4 is…
Ian Hincks
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singular value decomposition of a 2 x 2 complex matrix

This should be easy, but... I would like to express the singular value decomposition of a 2 x 2 complex matrix $A$ as function of its coefficients $A_{ij}$. In "closed form", no intermediate values, straight up. What I mean is that if I express the…
Ali K
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Computation of SVD of well-conditioned matrix takes more time than ill-conditioned matrix

I'm testing libraries for numerical computing and time they take to calculate SVD. During testing I encountered an issue for which I don't have an answer. I generated 2 matrices: random tall matrix using Matlab with function…
Intech
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